The best fighting games like Dynamite Cop are Die Hard Arcade, Streets of Rage 4 and Fight'N Rage. Below are 9, each with the reason it is here — and, at the end, what filtering to fighting costs you.
Filtering to fighting means you want a contest with a clear answer — you got it right or you did not. It is the right filter when what you liked was reading an opponent.
What you get: A skill ceiling you can actually see yourself climbing, and the shortest feedback loop in games.
What made Dynamite Cop worth playing in the first place is covered on the full list. This page is the fighting part of that answer, and only the fighting part.
The direct predecessor, and the same weapon-grabbing chaos.
The best modern beat-em-up, and it honours the arcade originals.
An indie brawler with branching routes and real depth.
The most fun four-player brawler in years.
For the improvised-weapon brawling, in a much bigger game.
Environmental weapons and hand-to-hand, made deadly serious.
Same arcade brevity, fantasy instead of skyscrapers.
Dreamcast contemporary where the stage is also the weapon.
Saturn brawler with branching paths and a huge cast.
A first few hours that can be discouraging alone. Fighting games are far better with someone at your level than against the internet.
The full list is on games like Dynamite Cop — 9 picks, no genre filter.
Die Hard Arcade. The direct predecessor, and the same weapon-grabbing chaos.
No. Dynamite Cop released on the Sega Dreamcast, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Much less than they were. Modern control schemes, rollback netcode and real single-player modes have changed the on-ramp completely in the last few years.
One opponent against one, or one against many. They share ancestry and almost nothing else — the picks below say which each one is.
By hand. Each pick was written for the full Dynamite Cop list first, on what the game actually does, and this page is the part of that list that is fighting — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the fighting guide for where to start in the genre generally.